A simple model for simulation of oxygen transport in the microcirculation

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Abstract
A mathematical model of deoxygenation of blood in the microcirculation is used to estimate the mass transfer resistance in the blood and to examine certain assumptions used in prior work on simulation of the microcirculation: the treatment of blood as a continuum and the use of a single-step reaction kinetics model. The erythrocytes are treated as cylindrical slugs which alternate with plasma gaps such that oxygen transport is by radial diffusion in the cell. The system of equations including reaction kinetics and oxyhemoglobin diffusion is solved numerically. The results are of direct applicability in estimation of oxygen concentration profiles in tissue. The results also indicate that the resistance to oxygen transport in the capillary (relative to that in the surrounding tissue) is much higher than predicted by the continuum approach used by most prior workers. The resistance in the capillary is a significant fraction of the overall resistance. Other results give quantitative estimates of the error incurred from use of a single-step kinetic model.